As a control device for a hybrid vehicle, a device is per se known (refer to Patent Document #1) that, during travel powered by an internal combustion engine, disconnects the engine with a clutch when the accelerator opening amount becomes less than or equal to a predetermined value, thereby changing over to an EV mode in which a motor-generator is used as the power source for propulsion. Moreover, for a hybrid vehicle that includes a differential mechanism that links together an engine and a motor-generator and a lock mechanism that changes over this differential mechanism between a differentiating state in which it permits a differentially rotating state between the engine and the motor-generator and a non-differentiating state in which it prohibits the differentially rotating state between the engine and the motor-generator, a control device is per se known (refer to Patent Document #2) that implements a differentiating mode in which propulsion using the engine is performed with the differential mechanism in the differentiating state, and a non-differentiating mode in which propulsion using the engine is performed with the differential mechanism in the non-differentiating state.